Involutions of Nikulin type. Nikulin showed that the involutions of a \(K3\) -surface \(X\)  that act as the identity on \(H^{2,0}(X)\)  are all alike: they have eight fixed points, so that the orbit space will have eight-double points, and resolving these double points produces a \(K3\) -surface. The K3 surfaces endowed with such an involution make up a single connected family. As Morrison [1]} observed, the action of the involution on their second homology is equivalent to the involution of the \(K3\) -lattice \(\mathbf {U}^{\oplus 3}\oplus \mathbf {E}_8(-1)^{\oplus 2}\)  that exchanges the last two summands. This motivates the following definition.
